Aspheric Surface Shape Error Correction Based on Modified Levenberg-Marquardt Algorithm

Jiannan Deng; Han Wang; Honghui Yao; Jiarong Zhang; Shaomu Zhuo; Xiaoqiang Yan

doi:10.3788/AOS202242.0512004

Acta Optica Sinica, Volume. 42, Issue 5, 0512004(2022)

Aspheric Surface Shape Error Correction Based on Modified Levenberg-Marquardt Algorithm

Jiannan Deng^1,2, Han Wang^1,2, Honghui Yao^2、*, Jiarong Zhang^1,2, Shaomu Zhuo^1,2, and Xiaoqiang Yan^1,2

¹State Key Laboratory of Precision Electronic Manufacturing Technology and Equipment, Guangzhou, Guangdong 510006, China

²Mechanical and Electrical Engineering, Guangdong University of Technology, Guangzhou, Guangdong 510006, China

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Figures & Tables(15)

Fig. 1. Different scanning modes. (a) Spiral scanning; (b) xy scanning; (c) raster scanning

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Fig. 2. Position error

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Fig. 3. Algorithm flowchart

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Fig. 4. Position error of ideal aspheric surface. (a) Front view of position error of ideal aspheric surface; (b) top view of position error of ideal aspheric surface; (c) front view of corrected aspheric surface; (d) top view of corrected aspheric surface

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Fig. 5. Surface shape after superimposing error. (a) Surface shape error; (b) surface shape after superimposing surface shape error and position error

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Fig. 6. UA3P surface shape measurement device

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Fig. 7. Surface shape comparison of lens G01. (a) Results of proposed algorithm (PV: 1.4483 μm, RMS: 0.3866 μm); (b) UA3P analysis results (PV: 1.4476 μm, RMS: 0.3866 μm)

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Fig. 8. Surface shape comparison of lens G02. (a) Results of proposed algorithm (PV: 0.6806 μm, RMS: 0.1952 μm); (b) UA3P analysis results (PV: 0.6807 μm, RMS: 0.1952 μm)

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Fig. 9. Surface shape comparison of lens G03. (a) Results of proposed algorithm (PV: 0.4031 μm, RMS: 0.0961 μm); (b) UA3P analysis results (PV: 0.4036 μm, RMS: 0.0961 μm)

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Fig. 10. Surface shape comparison of lens G04. (a) Results of proposed algorithm (PV: 0.6964 μm, RMS: 0.1699 μm); (b) UA3P analysis results (PV: 0.6959 μm, RMS: 0.1698 μm)

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Table 1. Aspheric coefficients

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Table 1. Aspheric coefficients

Aspheric coefficient	Accurate value	Aspheric coefficient	Accurate value
R	55.837020000	e₈	9.75997694×10^-11
k	8.551663247	e₁₀	-3.87517956×10^-14
e₂	0	e₁₂	-6.23460270×10^-18
e₄	8.78572651×10^-6	e₁₄	-1.42507364×10^-20
e₆	-3.13234400×10^-8	e₁₆	-2.48992698×10^-21

Table 2. Simulation results of ideal surface shape

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Table 2. Simulation results of ideal surface shape

Group	Positional parameter	Set value	Value obtained by proposed algorithm	Error
	α /(°)	5	5	0
	β /(°)	5	5	0
No. 1	Δx /mm	0.5	0.5	~0
	Δy /mm	0.5	0.5	~0
	Δz /mm	0.5	0.5	0
	α /(°)	1	1	0
	β /(°)	1	1	0
No. 2	Δx /mm	0.5	0.5	~0
	Δy /mm	0.5	0.5	~0
	Δz /mm	0.5	0.5	0

Table 3. Simulation results after superimposing error

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Table 3. Simulation results after superimposing error

Group	Positional parameter	Set value	Value obtained by proposed algorithm	Error
	α /(°)	5.000000000000000	4.999993073843890	6.926150×10^-6
	β /(°)	5.000000000000000	4.999992263189740	7.736810×10^-6
	Δx /mm	0.500000000000000	0.500004329863383	-4.329863×10^-6
No. 1	Δy /mm	0.500000000000000	0.500004849386064	-4.849386×10^-6
	Δz /mm	0.500000000000000	0.499999162227531	8.377720×10^-7
	PV /mm	0.000226446981615000	0.000226323408297924	1.235733×10^-7
	RMS /mm	2.80985136498203×10^-5	2.80974064194140×10^-5	1.107230×10^-9
	α /(°)	1.000000000000000	0.999995001684163	4.998310×10^-6
	β /(°)	1.000000000000000	0.999996651196207	3.348800×10^-6
	Δx /mm	0.500000000000000	0.500003323079212	-3.323070×10^-6
No. 2	Δy /mm	0.500000000000000	0.500003679484304	-3.679484×10^-6
	Δz /mm	0.500000000000000	0.499999708389944	2.916100×10^-7
	PV /mm	0.000238863720000000	0.000239647279737806	-7.835590×10^-7
	RMS /mm	2.82030650000000×10^-5	2.82010818746604×10^-5	1.983120×10^-9

Table 4. Parameters of different lenses

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Table 4. Parameters of different lenses

Aspheric coefficient	Lens
Aspheric coefficient	G01	G02	G03	G04
R	37.890940000	42.682000000	55.837020000	-16.151120000
k	10.224390000	-0.836000000	8.551663247	0.003262894
e₄	-1.53028180×10^-4	-7.72330620×10^-6	8.78572651×10^-6	-3.71860590×10^-5
e₆	2.3361022×10^-6	1.14160150×10^-8	-3.13234400×10^-8	3.17160760×10^-7
e₈	-1.59313600×10^-8	-9.71402170×10^-10	9.75997694×10^-11	7.22853940×10^-9
e₁₀	3.73855540×10^-10	-1.56805570×10^-12	-3.87517956×10^-14	2.97511920×10^-11
e₁₂	-1.25469080×10^-11	9.65786190×10^-14	-6.23460270×10^-18	-2.04783950×10^-13
e₁₄	1.04857130×10^-13	-3.80604700×10^-16	-1.42507364×10^-20	-5.68553110×10^-15
e₁₆	0	0	-2.48992698×10^-21	0
Effective caliber /mm	Ø16.93	Ø23.64	Ø32.80	Ø19.91

Table 5. Comparison of measurement results of different lenses

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Table 5. Comparison of measurement results of different lenses

Lens	PV /μm				RMS /μm
Lens	Proposed algorithm	UA3P	Error		Proposed algorithm	UA3P	Error
G01	1.44830			1.44760		0.00070		0.38660	0.38660	<0.10
G02	0.68060			0.68070		-0.00010		0.19518	0.19520	-0.02
G03	0.40310			0.40360		-0.00050		0.09610	0.09610	<0.10
G04	0.69640			0.69590		0.00050		0.16990	0.16980	0.10

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Jiannan Deng, Han Wang, Honghui Yao, Jiarong Zhang, Shaomu Zhuo, Xiaoqiang Yan. Aspheric Surface Shape Error Correction Based on Modified Levenberg-Marquardt Algorithm[J]. Acta Optica Sinica, 2022, 42(5): 0512004

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Paper Information

Category: Instrumentation, Measurement and Metrology

Received: Jul. 28, 2021

Accepted: Sep. 10, 2021

Published Online: Mar. 8, 2022

The Author Email: Yao Honghui (m13430351442@163.com)

DOI:10.3788/AOS202242.0512004

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology